We disagree again. The project plan is real, and it's more than a Gantt chart or Scrum or Kanban board. The project plan is supported by a budget, real dollars to be spent on materials and resources, including your labor. Most of the time, the programmers (and business analysts, and database specialists, and systems analysts, and....) tend to look at me as adding value to the project. As someone who has worked with all those areas in the past, I have enough knowledge of those areas to be able to understand the scope of the project, the risks involved, and present those in somewhat non-technical terms to the business. You know, the business,.....those people that allocate a budget to IT (for BAU, Business As Usual activities), and to IT projects. I'm sure you don't want those business folks looking over your shoulder and asking what you're doing and when will you be done every couple of days, but those business folks want to know that the money they're spending is providing value to the business. Hence, the PM is (amongst other things), a liason or buffer between IT and the business.
In short, just because the PM can't write code as well as you, it doesn't mean that the PM isn't adding value. As with most vehicles on the road, your mileage may vary, and not all PMs are equal. It's possible you have a bad PM. But it's also possible that you have tunnel vision and aren't seeing the big picture.
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